No, that's not "gotcha" logic. It's called a paradox.<quoted text>
God can't make something too heavy for Him to lift because He could lift anything He wants.
You think that's the GOTCHA logic?
There is no way to satisfy both parts of the question, either deity can make an object he can't life an therefore is not omnipotent, or he cannot make such an object and is not omnipotent.
A paradoxical property cannot exist for any entity, neither in reality nor in the imagination.
What you are experiencing is called cognitive dissonance.